Abstract
Based on Formal Concept Analysis the notion of a Temporal Conceptual Semantic System is introduced as a formal conceptual representation for temporal systems with arbitrary discrete or continuous semantic scales. In this paper, we start with an example of a weather map with a moving high pressure zone to explain the basic notions for Temporal Conceptual Semantic Systems. The central philosophical notion of an object is represented as a formal concept or, more flexible, as a tuple of concepts. Generalizing the idea of a volume of an object in physics we introduce the notion of a trace of an object in some space. This space is described as a continuous or discrete concept lattice. Combining the notion of a trace of an object with the notion of a time granule yields the notion of a state of an object at some time granule. This general notion of a state allows for a clear conceptual understanding of particles, waves and Heisenberg’s Uncertainty Relation. Besides these theoretical aspects, Temporal Conceptual Semantic Systems can be used very effectively in practice. That is shown for data of a distillation column using a nested transition diagram.
Supported by DFG project COMO, GZ: 436 RUS 113/829/0-1.
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References
Arbib, M.A.: Theory of Abstract Automata. Prentice Hall, Englewood Cliffs (1970)
Auletta, G.: Foundations and Interpretations of Quantum Mechanics. World Scientific Publishing Co. Pte. Ltd., Singapore (2000)
Becker, P.: Multi-dimensional Representation of Conceptual Hierarchies. In: Stumme, G., Mineau, G. (eds.) Proceedings of the 9th International Conference on Conceptual Structures, Supplementary Proceedings, pp. 33–46. Department of Computer Science, University Laval (2001)
Becker, P., Hereth Correia, J.: The ToscanaJ Suite for Implementing Conceptual Information Systems. In: Ganter, B., Stumme, G., Wille, R. (eds.) FCA 2005. LNCS (LNAI), vol. 3626, pp. 324–348. Springer, Heidelberg (2005)
Bertalanffy, L.v.: General System Theory. George Braziller, New York (1969)
Butterfield, J. (ed.): The Arguments of Time. Oxford University Press, Oxford (1999)
Butterfield, J., Isham, C.J.: On the Emergence of Time in Quantum Gravity. In: Butterfield, J. (ed.) The Arguments of Time. Oxford University Press, Oxford (1999)
Castellani, E. (ed.): Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton University Press, Princeton (1998)
Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press, London (1974)
Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999); German version: Springer, Heidelberg (1996)
Kalman, R.E., Falb, P.L., Arbib, M.A.: Topics in Mathematical System Theory. McGraw-Hill Book Company, New York (1969)
Lin, Y.: General Systems Theory: A Mathematical Approach. Kluwer Academic/Plenum Publishers, New York (1999)
Mesarovic, M.D., Takahara, Y.: General Systems Theory: Mathematical Foundations. Academic Press, London (1975)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Neumann, J.v.: Mathematical Foundations of Quantum Mechanics (engl. translation of Neumann, J.v.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932)). University Press, Princeton (1932)
Sowa, J.F.: Conceptual structures: information processing in mind and machine. Addison-Wesley, Reading (1984)
Sowa, J.F.: Knowledge representation: logical, philosophical, and computational foundations. Brooks Cole Publ. Comp., Pacific Grove (2000)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered sets, pp. 445–470. Reidel, Dordrecht (1982); Reprinted in: Ferré, S., Rudolph, S. (eds.): Formal Concept Analysis. ICFCA 2009. LNAI 5548, pp. 314–339. Springer, Heidelberg (2009)
Wille, R.: Conceptual Graphs and Formal Concept Analysis. In: Delugach, H.S., Keeler, M.A., Searle, L., Lukose, D., Sowa, J.F. (eds.) ICCS 1997. LNCS (LNAI), vol. 1257, pp. 290–303. Springer, Heidelberg (1997)
Wolff, K.E.: Concepts, States, and Systems. In: Dubois, D.M. (ed.) Proceedings of Computing Anticipatory Systems. American Institute of Physics, Conference, vol. 517, pp. 83–97 (2000)
Wolff, K.E.: A Conceptual View of Knowledge Bases in Rough Set Theory. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 220–228. Springer, Heidelberg (2001)
Wolff, K.E.: Temporal Concept Analysis. In: Mephu Nguifo, E., et al. (eds.) ICCS 2001 International Workshop on Concept Lattices-Based Theory, Methods and Tools for Knowledge Discovery in Databases, pp. 91–107. Stanford University, Palo Alto (2001)
Wolff, K.E.: Transitions in Conceptual Time Systems. International Journal of Computing Anticipatory Systems 11, 398–412 (2002)
Wolff, K.E.: Interpretation of Automata in Temporal Concept Analysis. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 341–353. Springer, Heidelberg (2002)
Wolff, K.E.: Concepts in Fuzzy Scaling Theory: Order and Granularity. Fuzzy Sets and Systems 132, 63–75 (2002)
Wolff, K.E.: ‘Particles’ and ‘Waves’ as Understood by Temporal Concept Analysis. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 126–141. Springer, Heidelberg (2004)
Wolff, K.E.: States, Transitions, and Life Tracks in Temporal Concept Analysis. In: Ganter, B., Stumme, G., Wille, R. (eds.) FCA 2005. LNCS (LNAI), vol. 3626, pp. 127–148. Springer, Heidelberg (2005)
Wolff, K.E.: States of Distributed Objects in Conceptual Semantic Systems. In: Dau, F., Mugnier, M.-L., Stumme, G. (eds.) ICCS 2005. LNCS (LNAI), vol. 3596, pp. 250–266. Springer, Heidelberg (2005)
Wolff, K.E.: A Conceptual Analogue of Heisenberg’s Uncertainty Relation. In: Ganter, B., Kwuida, L. (eds.) Contributions to ICFCA 2006, pp. 19–30. Verlag Allgemeine Wissenschaft (2006)
Wolff, K.E.: Conceptual Semantic Systems - Theory and Applications. In: Goncharov, S., Downey, R., Ono, H. (eds.) Mathematical Logic in Asia, pp. 287–300. World Scientific, New Jersey (2006)
Wolff, K.E.: Basic Notions in Temporal Conceptual Semantic Systems. In: Gély, A., Kuznetsov, S.O., Nourine, L., Schmidt, S.E. (eds.) Contributions to ICFCA 2007, pp. 97–120. Clermont-Ferrand, France (2007)
Wolff, K.E.: Applications of Temporal Conceptual Semantic Systems. In: Zagoruiko, N.G., Palchunov, D.E. (eds.) Knowledge - Ontology - Theory, vol. 2, pp. 3–16. Russian Academy of Sciences. Sobolev Institute for Mathematics, Novosibirsk (2007)
Wolff, K.E.: Relational Semantic Systems, Power Context Families, and Concept Graphs. In: Wolff, K.E., Rudolph, S., Ferré, S. (eds.) Contributions to ICFCA 2009, pp. 63–78. Verlag Allgemeine Wissenschaft, Darmstadt (2009)
Wolff, K.E.: Relational Scaling in Relational Semantic Systems. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009. LNCS (LNAI), vol. 5662, pp. 307–320. Springer, Heidelberg (2009)
Wolff, K.E.: Temporal Relational Semantic Systems. In: Croitoru, M., Ferré, S., Lukose, D. (eds.) ICCS 2010. LNCS (LNAI), vol. 6208, pp. 165–180. Springer, Heidelberg (2010)
Zadeh, L.A.: The Concept of State in System Theory. In: Mesarovic, M.D. (ed.) Views on General Systems Theory, pp. 39–50. John Wiley & Sons, New York (1964)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Part I: Inf. Science 8, 199–249, Part II: Inf. Science 8, 301–357; Part III: Inf. Science 9, 43–80 (1975)
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Wolff, K.E. (2011). Applications of Temporal Conceptual Semantic Systems. In: Wolff, K.E., Palchunov, D.E., Zagoruiko, N.G., Andelfinger, U. (eds) Knowledge Processing and Data Analysis. KPP KONT 2007 2007. Lecture Notes in Computer Science(), vol 6581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22140-8_5
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DOI: https://doi.org/10.1007/978-3-642-22140-8_5
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